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On the Grid Implementation of a Quantum

Reactive Scattering Program

Alessandro Costantini1, Dimitrios Skouteris1, Osvaldo Gervasi2

and Antonio Lagana1

1 Department of Chemistry, University of Perugia, Perugia, Italy2 Department of Mathematics and Informatics, University of Perugia,

Perugia, Italy

Lecture given at the

Joint EU-IndiaGrid/CompChem Grid Tutorial on

Chemical and Material Science Applications

Trieste, 15-18 September 2008

LNS0924009

[email protected]


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Abstract

Quantum reactive scattering codes are a family of calculations be-lieved to be less suited for the exploitation of the increasingly availableGrid computer power due to their large memory request. This is nottrue under proper circumstances and here the case of the ABC programthat has been efficiently implemented on the segment of the EGEE Gridavailable to the COMPCHEM Virtual Organization is discussed. Theimplementation was carried out in collaboration with the ApplicationPorting Support groups of MTI-SZTAKI and CESGA making use ofthe P-GRADE portal and of some java-based visualization tools.


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Contents

1 Introduction 149

2 ABC program description 150

3 A distributed quantum study of the F+HD reaction 151

4 The P-GRADE Grid implementation of ABC 153

5 A performance analysis 156

6 The improved rendering of ABC results 158

7 Conclusions 159

8 Aknowledgments 160


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On the Grid Implementation of a Quantum Reactive Scattering Program 149

1 Introduction

The possibility of exploiting Grid technologies to perform massive calcula-

tions has encouraged several researchers of the molecular science domain to

implement their programs on the Enabled Grid for E-sciencE (EGEE) envi-

ronment [1]. A family of calculations believed not to be completely suited to

exploit the increasing quantity of computer power being made available on

Grid platforms are those using quantum reactive scattering methods. The

high request of memory of quantum reactive scattering calculations, in fact,

makes related programs quite unsuitable for implementation on the Grid.

The overtaking of this difficulty is one of the missions of the Virtual Orga-nization (VO) COMPCHEM [2] and is also the primary goal of QDYN, the

working group of the COST Action D37 [3] coordinated by the Computa-

tional Dynamics and Kinetics Research Group of the University of Perugia.

In this lecture, in order to illustrate the process of porting on the Grid

a quantum mechanical reactive scattering code, we consider the ABC atom-

diatom reactive program [4] that carries out accurate time independent cal-

culations of the quantum S matrix elements from which reaction probabilities

as well as state-to-state integral and differential cross sections can be eval-

uated. The ABC code, in addition to a significant memory request, has a

quite large CPU demand. Moreover, it is seldomly used for just one set of pa-

rameters. In a typical use case, the ABC program must be executed severaltimes for different sets of input parameter (like initial states and collision en-

ergies) consuming a large amount of CPU time. This feature, indeed, makes

it suitable for parameter study runs provided that the machines chosen for

the calculation have a memory sufficiently large to host the matrices used

by the program.

For this reason ABC has been considered for gridification. To this end

both low and high level gridification tools were used. At low level some

procedures specifically implemented to run ABC on the Grid were used.

At upper level the P-GRADE Grid Portal [5,6] was used in collaboration

with the Grid Application Support Centre (GASuC) of the MTA SZTAKI

[7]. P-GRADE is available on all the major Globus, LCG and gLite based

production Grids [8]. To make the Grid application more user friendly the

gridified version of ABC was also dressed with some graphic utilities.

Accordingly, in section 2 we describe the ABC program, in section 3 we

present a typical calculation at a low level of gridification, in section 4 we

discuss the P-GRADE high level gridification, in section 5 we analyse related


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150 A. Costantini, D. Skouteris, O. Gervasi and A. Lagana

performances, and in section 6 we discuss the implementation of a more userfriendly rendering of the results.

2 ABC program description

The ABC program integrates the atom-diatom Schrodinger equation for re-

active scattering problems using Delves hyperspherical coordinates [9] and

a coupled channel method. The program integrates the time independent

atom-diatom Schrodinger equation of the nuclei:

[T + V E] = 0 (1)

with T being the kinetic operator, V the potential and E the total energy.

In eq. 1 is the nuclear wavefunction (depending on nuclear coordinates

only) that in ABC is expanded in terms of the hyperspherical arrangement

channel basis functions. The channel basis functions BJMj are also

labeled after J (the total angular momentum quantum number), M and (the space- and body- fixed projections of J), and j the vibrational and

rotational quantum numbers of the asymptotic channel. They also depend

on the three Euler angles, the Jacobi orientation angle and the internal

Delves hyperspherical angle D. In order to carry out the propagation of

the solution from the strong interaction region to the asymptotes, one needsto integrate, through the sectors of the various regions in which the reaction

coordinate has been segmented, the equations

d2g

d2= O1Ug. (2)

which relate the second derivative with respect of the hyperspherical radius

link the matrix of the coefficients (g) of the already mentioned expansion

to the g matrix via the overlap matrix O whose elements are formulated as

O

j

j= BJMj |B

JM

j

(3)

and the coupling matrix U whose elements are formulated as

U

j

j= BJMj |

2

2(H E)

1

42|BJM

j

. (4)

In eq. 4 is the reduced mass of the system and H is the part of the

Hamiltonian not containing derivatives with respect to .


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To integrate the set of coupled differential equations given in eq. 2the interval of is segmented in sectors whose local bound state func-

tions are calculated by diagonalizing a Hamiltonian which describes related

D-dependent motions using a carefully chosen reference potential. The

coupled-channel equations are integrated starting from small values of (by

propagating the solution first within the sector and then chaining its value

at the end of the sector with that at the beginning of the next one) to the

asymptotes. At the asymptotes the solutions are matched to both reactant

and product states and the related S matrix is evaluated. Finally, from the

calculated S matrix elements reactive probabilities can be worked out and

some observable properties are determinated.

3 A distributed quantum study of the F+HD

reaction

The key features of the ABC program relevant for gridification are easily

illustrated by considering the F + HD bench reaction. The computational

investigation of the F + HD reaction can be performed by carrying out the

calculation of its reactive properties using an extremely fine energy Grid of

energy (so as to easily single out even the width of narrow resonances) for

the zero total angular momentum (J = 0 given as jtot in Table 1 in whichthe namelist of all input data is listed) case.

This case study is actually ideal to show the particular importance of

distributed concurrent computing for the characterization of atom-diatom

reactive resonances in the threshold region that is ideally suited for a pa-

rameter sweeping study. A resonance falling in this energy region when using

a potential energy surface called SW might, in fact, survive to the total an-

gular momentum averaging and show up in the plot of the integral cross

section as a function of energy for a comparison with the experiment [ 10].

A Grid based parameter sweeping study is, therefore, of paramount impor-

tance to enable the calculation of the probability on a very large set of finegrained energy values. In this way the problem is transformed from that

of having enough computing time to the one of having enough computing

elements. In the low level distribution of the calculation of the Grid a set

of scripts has been created in order to automatically manage the submission

and the retrieval of the submitted jobs.

In the first step two files are created namely: grid server (which contains


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the name of the queues and the machines in which the job is going to beexecuted) and job mask (which contains all the needed information about

the jobs and the associated submission status).

In the second step all the jobs are submitted to the Grid and their status

is periodically checked making use of the crontab command. If a job is

abnormally ended or aborted, the script resubmits it updating the job mask

file. In this step the machine queue to which the job is to be submitted is

randomly chosen from the list stored in the grid server file.

In the third step, after the job is correctly finished, a retrieve command

is launched in order to collect all the output files produced by the calculation

saving them in a specific directory. The procedure includes also a check ofthe information retrieved to make sure that the ABC program has ended

correctly.

In Table 1 the maximum value of (rmax), the number of sectors (mtr),

the initial value of total energy (enrg) and the energy increment (dnrg)

chosen for the calculations are also given. The atomic masses (mass) given

Table 1: Input parameters for the test calculation on the F + HD(=0,j=0)reaction.

Parameter Explanationmass = 19,1,2 Masses of the three atoms in atomic mass units.jtot = 0 Total angular momentum quantum number J.ipar = 1 Triatomic parity eigenvalue P.

jpar = 0 Diatomic parity eigenvalue p.emax = 1.7 Maximum internal energy in any channel (in eV).jmax = 15 Maximum rotational quantum number of any channel.kmax = 4 Helicity truncation parameter kmax.rmax = 12.0 Maximum hyperradius max (in bohr).

mtr = 150 Number of log derivative propagation sectors.enrg = 0.233 Initial scattering energy (in eV).

dnrg = 0.001 Scattering energy increment (in eV).nnrg = 48 Total number of scattering energies.nout = 0 Maximum value of for which output is required.

jout = 0 Maximum value of j for which output is required.

in the first line of the Table can be integer (the program adds more significant


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figures automatically) and if no PES is specified a default one (SW of [ 11])is chosen for the calculations. The parameter jpar is not used for the F

+ HD reaction, since it has a meaning only for the symmetric A + B2reactions. Similarly, the parameter ipar, that has a meaning only for the

totally symmetric reaction A + A2, is not used. The helicity truncation

parameter kmax is also not used when J=0 since it has a meaning only for

J > 0. The value ofkmax given in the table is the one necessary to calculate

converged integral and differential cross sections for the F + HD ( = 0,

j = 0) reaction at collision energies slightly higher than those considered

here [12] whereas emax and jmax represent the upper limits considered for

total energy and the diatomic rotational quantum number. Due to the highnumber of values of the scattering energy (nnrg) allowed for the calculation

by the exploitation of concurrent computing on the Grid, we obtain a rather

long output file whose key information are summarized in Figs. 1 and 2.

An important aspect extracted from the many details of the calculations is

the evidence that, as already pointed out in ref. [10] at an energy of 0.254

eV, a pronounced quantum mechanical resonance takes places when F + HD

reacts (see the upper panel of Fig. 1 where state-to-state probabilities for

the two possible products are plotted as a function of the total energy E).

The figure shows a high resonance peak (more than 0.5) only for the = 0

to = 2 transition of the process leading to HF (see left-hand side panels of

Fig. 1). On the contrary, no resonant peaks are shown by the state-to-stateprobabilities of the process leading to DF (right-hand side panels of Fig. 1).

The product rotational distribution associated to the resonant transition is

remarkably broad, as shown in Fig. 2.

4 The P-GRADE Grid implementation of ABC

As a next step ABC was implemented on the COMPCHEM User Interface

(ui.grid.unipg.it) using the P-GRADE Grid Portal [5]. P-GRADE (release

2.7) provides graphical tools and services supporting Grid application de-

velopers in porting legacy programs onto the Grid without necessarily re-engineering or modifying the code. It enables, in fact, to define a parameter

study application structure in a graphical environment and, based on this de-

scription, it generates the Grid specific scripts and commands which actually

carry out the execution on the distributed Grid platform. The generic struc-

ture of the P-GRADE Grid Portal application is a workflow that integrates

batch programs into a directed acyclic graph by connecting them together


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Figure 1: State-to-state reaction probabilities for F + HD( = j = 0) HF() + D(left-hand side panels) and DF() + H (right-hand side panels) reactions calculated onthe SW potential energy surface at J = 0.

with file channels. A batch component can be any executable code which is

binary compatible with the underlying Grid resources (typically with Globusand EGEE clusters). A file channel defines directed data flows between two

batch components and specifies that the output file of the source program

must be used as the input file of the target program. The workflow manager

subsystem of P-GRADE resolves such dependencies during its execution by

transferring and renaming files. A screen-shot of the P-GRADE Grid Portal

implemented on COMPCHEM user interface and accessible to the user after

the login procedure, is shown in Fig. 3 for four testing workflows.

The workflow developed for that purpose is shown in the left-hand side

panel of Fig. 4. As shown by the figure the workflow is articulated in three

different components represented as large boxes named Generator, Ex-ecutor and Collector. For the case study discussed here the convergence

checks with the increase of the number of rotational states and with the size

of the hyperradius are analyzed. In our study various copies of the ABC

program having different Maximum rotational and Maximum hyperra-

dius length (see the right-hand side panel of Fig. 4) in a typical parameter

study fashion to check for convergence were executed. In this case the Gen-


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Figure 2: Product rotational distribution of the F + HD( = j = 0) HF( = 2, j)+ D reaction calculated on the SW potential energy surface at the energy E=0.254 eV ofthe maximum of the resonant peak at J = 0.

erator produces all the necessary permutations of the jmax and rmax values

and stores them in the input files. These files are then used as input data

when they are staged to Grid resources and the sequential ABC code (imple-mented as a single Fortran 90 executable) runs. In the left-hand side region

of Figure 4 the small boxes placed by side to the components represent the

input/output files prepared for the FORTRAN program by the workflow

manager of P-GRADE which are used/produced by the Fortran code and

are then transferred to the EGEE Computing Element. This makes the ex-

ecutable need neither to know anything about the Grid configuration nor to

be modified. Finally, the third component, the Collector, is responsible for

collecting the results of the parameter study, analyzing them and creating a

typical user friendly filtered result (to be considered as the final result of the

simulation) without carrying out any post-processing. It simply collects theresults from the ABC jobs and compresses the files into a single archive file

that can be downloaded to the user through the Portal web interface. The

purpose of this step is, in fact, to make the access to results more convenient

for the end users.

In our case the workflow structure was defined and the executable and

input components for the workflow nodes were produced, the ABC code was


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run with multiple input data sets on the section of the production EGEEGrid infrastructure available to the COMPCHEM VO. Using the Workflow

Manager window of P-GRADE (Fig. 5), the user was able to perform all

the actions related to the chosen workflow (submission, abortion, resuming)

and monitor the status of the job with the possibility of checking the log file

produced at every step in case of error. From the same window the user is

also able to directly download the results coming from the calculations by

pressing the green button located under the Output field.

Figure 3: A screen-shot of the fully functional P-GRADE Grid Portal 2.7 installed onthe COMPCHEM user interface.

5 A performance analysis

To provide the students of the school with a case study to evaluate the

performance of the P-GRADE Grid procedure implemented for ABC, theinput generation, the concurrent run of the code on several Grid resources,

and the output collection were executed for the already mentioned bench

system. Since the execution time of both the generator and the collector

stages showed to be negligible compared with that of the ABC code, the

discussion will be confined to the latter. The execution of the ABC program

on a single Intel Pentium 4 machine with 3.4 GHz CPU and 1 Gbyte memory


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Figure 4: A screen-shot of the workflow prototype components generated by the auto-matic Generator of P-GRADE.

Figure 5: A screen-shot of the Workflow Manager window of the P-GRADE Grid Portal.

takes from 3 to 6 hours, depending on the chosen values of jmax and rmax.

When using the EGEE Grid platform one has to add to it an approximately


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even amount of time for the job to queue on the Grid resource. This meansthat the average execution time of an ABC job on the Grid is about twice

as long as the one on a dedicated local machine that is equivalent to say

that the Grid execution of a job totals an average of about 5 hours per

job. This also means that the break even between a local single machine

and a concurrent Grid execution is reached as soon as there are at least 2

ABC jobs in a simulation. This means also that the throughput gain rapidly

approaches the number of available machines provided that the variability

of the parameter on which the distribution is carried out is large enough to

accomodate an equal number of jobs.

As a matter of fact it has to be pointed out here that the selection of theDO LOOP to distribute is a critical choice for the exploitation of concur-

rency. It is therefore apparent that the choice made in the above discussed

bench run does not fully exploit the potentialities of the ABC concurrency

since it is clearly targeted to convergence studies (usually performed once

for ever at the beginning of an investigation) and not to production runs and

related massive computational campaigns. In production runs, in fact, it is

more appropriate to exploit, for example, the concurrency achieved when it-

erating on the collision energy enrg values. For this purpose it is, therefore,

important to wrap ABC in a way that the concurrency on this parameter is

exploited.

6 The improved rendering of ABC results

In a Grid approach in which most of the computational effort is distributed

on the net it is appropriate to equipe the user machine for a more user

friendly rendering of the results. For this purpose, as already mentioned in

collaboration with CESGA [13], additional efforts were spent to improve the

rendering of the ABC results. The efforts concentrated on the construction

of a prototype web portal able to analyze the ABC output files which are

arranged so as to be supported by the P-GRADE system. For this purpose

a demo portlet prepared for Gridsphere (the same technology on which P-GRADE is based) was adapted in order to enable the drawing of 2D-Graph

rendering of the Reaction Probabilities for each individual output file and

was deployed on P-GRADE. The assembled prototype provides the users

with the option of plotting the reaction probabilities as a function at the

same time of energy and quantum states. A typical output of this type for

the bench system is given in Fig. 6. There, the F + HD reactive probability


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is plotted as a function of the collision energy and a given rotational state.The implemented portlet has been written entirely in java and makes use

of external bash scripts in order to:

- list the workflows present on the users home

- unpack and list the the packed file which contains all the output files

for a single workflow

- extract all the needed data from the selected output file and process

them in order to obtain a data format usable for the visualization.

The External Portlet is shown in Fig 6. After a single workflow has been

completed, the user can go to the Externals Portlets, upload the workflow

list with the related button and copy and paste the selected one on the

first blank space before pressing the Job list button. After that the job

list appears on the screen and the user needs to repeat the copy-and-paste

procedure choosing a job output and put it on the second blank space. At

this point the workflow and the related job have been selected and the 2D-

Graph can be rendered. In this way the final user can compare the Reaction

Probabilities for a selected atom-diatom reaction (with no need to download

all the output files which remain on the server) and evaluate the possible

strategies for a new calculation.

7 Conclusions

The study has tackled the problem of implementing a time independent

quantum reactive scattering application on the EGEE Grid environment of

the reactive properties of the F + HD reaction. This has been carried out

by the porting of the ABC atom-diatom time independent quantum reac-

tive scattering code on the Grid and by benchmarking it through massive

calculations. This has been made possible by a collaboration of our De-

partment with both the Application Porting group of EGEE and CESGA.As a result, extended measurements of the performance of the P-GRADE

portal when carrying out massive calculations of the detailed probabilities

of atom-diatom reactions were made and the friendliness of the rendering

of the calculated results was improved. This has allowed us to show that

although the competition for job slots on the EGEE Grid can make the ex-

ecution of a single ABC run twice as slow with respect to that measured on


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Figure 6: A screen-shot of the new Extra Portlet window of the P-GRADE Grid Portalin which the Reaction Probabilities 2D-Graph is rendered.

a local machine, the overall execution time rapidly approaches the number

of the computing elements used. At the same time it has shown that the

consequent relief of the user machine can be usefully exploited to improve

the friendliness of the results rendered.

8 Aknowledgments

This work makes use of results produced by the EGEE-III project (contract

number IST-2003-508833). The work exploits also the results of research

projects funded by ESA (contract number 21790/08/NL/HE) MIUR, CNR

and COST in Chemistry.


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References

[1] EGEE website: http://public.eu-egee.org

[2] COMPCHEM website: http://compchem.unipg.it

[3] QDYN is the working group n. 2 of the CMST COST Action D37:

http://www.cost.esf.org/index.php?id=189&action number=D37

[4] D. Skouteris, J.F. Castillo and D.E. Manolopulos, (2000). ABC: a quan-

tum reactive scattering program. Comp. Phys. Comm. 133 128-135

[5] P-GRADE Grid Portal: http://portal.p-grade.hu

[6] G. Sipos and P. Kacsuk, (2006). Multi-Grid, Multi-User Workflows in

the P-GRADE Portal. Journal of Grid Computing, Vol. 3, No. 3-4,

Kluwer Academic Publishers, pp. 221-238

[7] GASuC (Grid Application Support Centre):

http://www.lpds.sztaki.hu/gasuc

[8] gLite website: http://glite.web.cern.ch/glite

[9] G.C. Schatz, (1998). Quantum reactive scattering using hyperspherical

coordinates: results for H + H2 and Cl + HCl. Chem. Phys. Lett. 15092-98

[10] R.T. Skodje, D. Skouteris, D.E. Manolopulos, S.-H. Lee, F. Dong and

K. Liu, (2000). Resonance-mediated chemical reaction: F + HD to HF

+ D. J. Chem. Phys. 112 4536-4552

[11] K. Stark and H.-J. Werner, (1996). An accurate multireference config-

uration interaction (MRCI) calculation of the potential energy surface

for the F + H2 - HF + H reaction. J. Chem. Phys. 104 6515-

[12] J.F. Castillo and D.E. Manolopulos, (1998). Quantum mechanical angu-

lar distributions for the F+HD reaction. Faraday Discuss. Chem. Soc.110 119-138

[13] http://www.cesga.es

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